Early Universe Test of Nonextensive Statistics

Torres, D. F.; Vucetich, H.; Plastino, A.

doi:10.1103/physrevlett.79.1588

Cited by 135 publications

(107 citation statements)

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“…Under the assumption that expression (2) [and therefore (7)] can be applied to the equilibrium distributions and thus to S ‫ء‬ , we can substitute S ‫ء‬ ͑A͒ by S ‫ء‬ ͕͑͗X a ͘ q ͖͒. Differentiating the expression (7) with respect to l and taking l 1 we obtain…”

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confidence: 99%

“…This results from the assumption of nonadditive statistical entropies and the maximum statistical entropy principle, following the information theory formulation of statistical mechanics proposed by Jaynes [4]. Indeed, besides its relevance in many nonequilibrium problems, nonextensivity is of interest for systems of particles which show longrange interactions [5], as occurs in a number of ferroic materials [6] such as ferromagnetic, ferroelastic, ferroelectric solids, and astrophysical systems [7]. Within this framework, the Tsallis statistical entropy [8] has proven to be the only nonadditive generalization of Gibbs-Shannon entropy which satisfies the following properties: (i) positivity (it takes zero value for absolute certainty), increasing monotonously with increasing uncertainty, and (ii) concavity.…”

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Is Tsallis Thermodynamics Nonextensive?

Vives

Planes

2001

Phys. Rev. Lett.

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Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einstein's formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. The use of the proposed transformation of variables also shows that fluctuations within Tsallis statistics can be mapped to those of standard statistical mechanics. DOI: 10.1103/PhysRevLett.88.020601 PACS numbers: 05.70.Ln, 05.20.Gg, 05.40. -a During the past few years there has been a great deal of interest in studying nonextensive thermodynamics [1][2][3]. This results from the assumption of nonadditive statistical entropies and the maximum statistical entropy principle, following the information theory formulation of statistical mechanics proposed by Jaynes [4]. Indeed, besides its relevance in many nonequilibrium problems, nonextensivity is of interest for systems of particles which show longrange interactions [5], as occurs in a number of ferroic materials [6] such as ferromagnetic, ferroelastic, ferroelectric solids, and astrophysical systems [7]. Within this framework, the Tsallis statistical entropy [8] has proven to be the only nonadditive generalization of Gibbs-Shannon entropy which satisfies the following properties: (i) positivity (it takes zero value for absolute certainty), increasing monotonously with increasing uncertainty, and (ii) concavity. However, many fundamental features regarding the connection between the formulation of statistical mechanics and thermodynamics remain unclear. For instance, the identification of adequate generalized thermodynamic forces and the computation of statistical fluctuations are still controversial [9]. In this Letter we clarify such problems and provide robust arguments showing the equivalence of the present formulations of nonextensive Tsallis thermodynamics with the standard extensive equilibrium formulation.Within the Tsallis formalism, the lack of information associated with any probability distribution ͕p͑i͖͒ defined on a set of microstates V ͕i͖ [10] is given bywhere the parameter q, determining the degree of nonextensivity, is positive in order to ensure the concavity of S . The q-logarithmic function is defined as ln q f ͑ f 12q 2 1͒͑͞1 2 q͒. In the q ! 1 limit, Eq. (1) reduces to the Gibbs-Shannon entropy S 2 P i p͑i͒ lnp͑i͒. In order to simplify the notation, we will indicate the set V only when necessary. The novelty of the statistical entropy (1) is that it does not satisfy additivity. Instead, for two systems A and B described by independent probability distributions,For a given physical system the equilibrium probability distribution ͕p ‫ء‬ ͑i͖͒ corresponds to the distribution that maximizes S under the normalization condition1͔ and the relevant constraints imposed by the available statistical information on the system. The thermodynamic equilibrium entr...

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Is Tsallis Thermodynamics Nonextensive?

Vives

Planes

2001

Phys. Rev. Lett.

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“…Space plasma observations clearly indicate the presence of ion and electron populations that are far away from their thermodynamic equilibrium. [23][24][25][26][27][28][29][30] A new statistical approach, namely nonextensive statistics or Tsallis statistics based on the derivation of Boltzmann-Gibbs-Shannon (BGS) entropic measure, is proposed to study the cases where Maxwell distribution is considered inappropriate. This was first acknowledged by Reni and afterwards proposed by Tsallis.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear ion‐acoustic cnoidal wave in electron‐positron‐ion plasma with nonextensive electrons

Farhadkiyaei

Dorranian

2017

Contrib. Plasma Phys

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Effects of plasma nonextensivity on the nonlinear cnoidal ion-acoustic wave in unmagnetized electron-positron-ion plasma have been investigated theoretically. Plasma positrons are taken to be Maxwellian, while the nonextensivity distribution function was used to describe the plasma electrons. The known reductive perturbation method was employed to extract the KdV equation from the basic equations of the model. Sagdeev potential, as well as the cnoidal wave solution of the KdV equation, has been discussed in detail. We have shown that the ion-acoustic periodic (cnoidal) wave is formed only for values of the strength of nonextensivity (q). The q allowable range is shifted by changing the positron concentration (p) and the temperature ratio of electron to positron ( ). For all of the acceptable values of q, the cnoidal ion-acoustic wave is compressive. Results show that ion-acoustic wave is strongly influenced by the electron nonextensivity, the positron concentration, and the temperature ratio of electron to positron. In this work, we have investigated the effects of q, p, and on the characteristics of the ion-acoustic periodic (cnoidal) wave, such as the amplitude, wavelength, and frequency. KEYWORDScnoidal wave, electron-positron-ion plasma, ion-acoustic nonlinear wave, plasma nonextensivity, solitary wave INTRODUCTIONPlasma is mainly the science of universe, new accelerators, and new source of energy. Furthermore, there are many other applications of plasma that is penetrating into the technology of our ordinary life. [1,2] Plasma is a multimode medium. Depending on plasma species and condition, as well as plasma energy, a wide range of longitudinal or transverse modes in cnoidal or soliton form may generate in plasma medium. Some of them may be observed in linear regime, but there are a large number of plasma modes that will appear after taking the nonlinearity into account. Because of its high energy, the nonlinear phenomena play an essential role in plasma medium.Normal plasmas comprise of electrons, ions, and neutral particles. In the case of high-energy plasma, positrons will be produced in the medium due to pair production phenomena. The electron-positron-ion (e-p-i) plasma has an important role in the understanding of the plasmas in the early universe, [3,4] in active galactic nuclei, [5] in pulsar magnetospheres, [6,7] and in the solar atmosphere.[8] It is well known that when positrons are introduced into e-i plasma, the response of the plasma changes significantly. The presence of positrons has some application in plasma. For instance, they can be used to probe particle transport in tokamaks, and since they have sufficient lifetime, the two-component (e-i) plasma becomes three-component (e-p-i) plasma. [9][10][11][12][13] Most of the astrophysical plasmas also contain positrons in addition to electrons and ions. During the last decade, e-p-i plasma has attracted the attention of several authors. They have studied the linear and nonlinear wave propagation in e-p-i plasmas using different models. [14][1...

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“…Amongst them stellar polytrops [3], Levylike anomalous diffusions [4], two dimensional turbulance [5], solar neutrino problem [6] velocity distribution of galaxy clusters [7], Cosmic background radiation [8,9] and correlated themes [10], linear response theory [11], thermalization of electron-phonon system [12], and low dimensional dissipative systems [13] could be enumareted It should be remarked that what makes S q favourable is that it has, with regard to {p i }, definite concavity property for all values of q [ 14].…”

Section: Introductionmentioning

confidence: 99%